Finding Plans and Heuristics with Spectral Graph Theory

Johannes Schmalz

Track: Long Paper (9 pages including references)

Previous Publication: No, the submission has not been published or accepted at another conference.

Keywords: spectral graph theory, plans, network flow

Abstract: Spectral graph theory can be used to construct plans and heuristics for undirected graphs with a goal. A recent algorithm computes the smallest eigenvector of a graph's Dirichlet Laplacian matrix and interprets this eigenvector as a heuristic function over the graph's vertices -- greedily following this heuristic is guaranteed to lead to the goal. In this paper, we show that finding the smallest eigenvector is equivalent to finding a network flow over the graph, and then it becomes intuitively clear that following the flow must lead to the goal. We also show that the eigenvector produces a consistent, goal-aware heuristic, and discuss how this approach may be applicable to planning.

Submission Number: 12